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1、万有引力定律
1、定义：两个物体间的引力大 小，与它们的质量乘积成正比，与它们距离的平方成反比
2、公式：$ F=G \frac{m_1m_2}{r^{2} } $
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1、引入多个坐标系的原因

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1、万有引力定律
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2、公式：$ F=G \frac{m_1m_2}{r^{2} } $
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1、定义：两个物体间的引力大 小，与它们的质量乘积成正比，与它们距离的平方成反比
2、公式：$ F=G \frac{m_1m_2}{r^{2} } $
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1、引入多个坐标系的原因

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                                <h2>
                                    2.1 坐标系
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                                    2023-09-14, 1154 words, 5 min read
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                                        <h2 id="一-力学基础">一、力学基础</h2>
<h4 id="1-万有引力定律">1、万有引力定律</h4>
<p>1、定义：两个物体间的引力大 小，与它们的质量乘积成正比，与它们距离的平方成反比</p>
<p>2、公式：$ F=G \frac{m_1m_2}{r^{2} } $</p>
<h2 id="二-惯性导航常用的坐标系">二、惯性导航常用的坐标系</h2>
<h4 id="1-引入多个坐标系的原因">1、引入多个坐标系的原因</h4>
<ul>
<li>通常将一个物体抽象为一个坐标系来表示。一个物体相对于另一个物体的运动，就相当于一个坐标系在空间相对于另一个坐标系的运动。</li>
<li>在惯导系统中，研究惯性元器件（陀螺仪、 加速度计）、惯性导航系统或运载体的运动时，也是通过两套适当的坐标系之间的关系来实现。</li>
</ul>
<h4 id="2-惯性坐标系">2、惯性坐标系</h4>
<p>1、参考坐标系：一套坐标系与被研究对象相连结，另一套坐标系与选定的参考空间相连结，后者构成了前者运动时的参考坐标系</p>
<p>2、参考坐标系要求：惯性坐标系（在惯性空间中保持静止或匀速直线运动为参照物构成的参照系。此时，牛二才成立）。</p>
<p>2、真正的惯性系不存在</p>
<h4 id="2-太阳中心惯性坐标系s">2、太阳中心惯性坐标系S</h4>
<p>1、定义：以太阳中心作为坐标系的原点，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Z</mi><mi>s</mi></msub></mrow><annotation encoding="application/x-tex">Z_s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴垂直于地球公转轨道平面，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>s</mi></msub></mrow><annotation encoding="application/x-tex">X_s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>和<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Y</mi><mi>s</mi></msub></mrow><annotation encoding="application/x-tex">Y_s</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴在地球公转轨道平面，构成右手坐标系</p>
<p>2、适用性：星际间运载体的导航定位</p>
<img src="http://cos.pansis.site/202309142236217.png" alt="image-20230914223634132" style="zoom:33%;" />
<h4 id="3-地心惯性坐标系i">3、地心惯性坐标系i</h4>
<p>1、定义：以地球地心作为坐标系原点，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Z</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">Z_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴沿地球自转轴，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>i</mi></msub><mi mathvariant="normal">、</mi><msub><mi>Y</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">X_i、Y_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord cjk_fallback">、</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴在赤道平面，构成右手直角坐标系。</p>
<p>2、适用性：当研究地球表面附近的载体导航定位问题时，多采用该惯性坐标系。</p>
<img src="http://cos.pansis.site/202309142239390.png" alt="image-20230914223902334" style="zoom:33%;" />
<h4 id="4-地球坐标系e">4、地球坐标系e</h4>
<p>1、定义：以地球地心作为坐标系原点，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Z</mi><mi>e</mi></msub></mrow><annotation encoding="application/x-tex">Z_e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴沿极轴方向，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>e</mi></msub></mrow><annotation encoding="application/x-tex">X_e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴在赤道平面与本初子午面的交线上，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Y</mi><mi>e</mi></msub></mrow><annotation encoding="application/x-tex">Y_e</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">e</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴也在赤道平面上，并构成右手直角坐标系。（随着地球转）</p>
<img src="http://cos.pansis.site/202309142239150.png" style="zoom: 50%;" />
<p>2、一年中，地球相对于太阳自转了365+0.25周。转一周（太阳日）是24小时。</p>
<p>​      一年中，地球相对于恒星自转了366+0.25周。转一周（恒星日）少于24小时。（约为23 小时56分4.09秒）</p>
<p>​</p>
<h4 id="5-地理坐标系t">5、地理坐标系t</h4>
<p>1、定义：以运载体所在的点为原点，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">X_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴沿当地纬线指东，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Y</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">Y_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴沿当地子午线指北，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Z</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">Z_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>沿当地地理垂线指上，构成右手直角坐标系。</p>
<img src="http://cos.pansis.site/202309142243003.png" alt="image-20230914224356949" style="zoom:33%;" />
<p>2、当地水平面：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">X_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴和<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Y</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">Y_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴构成当地水平面</p>
<p>​       当地子午面：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Y</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">Y_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴和<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Z</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">Z_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2805559999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴构成当地子午面</p>
<p>3、运载体相对地球运动 将相当于地理坐标系相对地 球坐标系运动（转动）。</p>
<p>4、地理坐标系相对于惯性参考系的转动角速度可分为两部分</p>
<p>地理坐标系相对于地球坐标系的转动角速度（主要研究）</p>
<p>地球坐标系相对于惯性参考系的转动角速度</p>
<h4 id="6-载体坐标系b">6、载体坐标系b</h4>
<p>1、定义：以运载体所在的点为原点，</p>
<p>（对于飞机、舰船等巡航式运载体）<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>X</mi><mi>b</mi></msub></mrow><annotation encoding="application/x-tex">X_b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.07847em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>轴沿运载体横轴指右，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Y</mi><mi>b</mi></msub></mrow><annotation encoding="application/x-tex">Y_b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.22222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>沿运载体纵轴指前，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>Z</mi><mi>b</mi></msub></mrow><annotation encoding="application/x-tex">Z_b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07153em;">Z</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>沿运载体竖轴，构成右手直角坐标系。</p>
<img src="http://cos.pansis.site/202309142326750.png" alt="image-20230914232641701" style="zoom:33%;" />
<h2 id="三-地理坐标系相对于惯性参考系的转动角速度计算">三、地理坐标系相对于惯性参考系的转动角速度计算</h2>
<h4 id="1-角速度分解">1、角速度分解</h4>
<p>地理坐标系相对于惯性参考系的转动角速度可分为两部分</p>
<ul>
<li>地理坐标系相对于地球坐标系的转动角速度（主要研究）</li>
<li>地球坐标系相对于惯性参考系的转动角速度</li>
</ul>
<h4 id="2-地理坐标系相对于地球坐标系的转动角速度">2、地理坐标系相对于地球坐标系的转动角速度</h4>
<p>设运载体所在地的纬度为$\varphi $， 航行高度为 <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>h</mi></mrow><annotation encoding="application/x-tex">h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">h</span></span></span></span>，速度为<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span></span></span></span> ，航向角为<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ψ</mi></mrow><annotation encoding="application/x-tex">\psi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">ψ</span></span></span></span> 。</p>
<img src="http://cos.pansis.site/202309142255218.png" alt="image-20230914225548181" style="zoom:33%;" />
<ul>
<li>将<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span></span></span></span>沿沿地理北向和东向进行分解</li>
</ul>
<img src="http://cos.pansis.site/202309142253896.png" alt="image-20230914225348862" style="zoom:33%;" />
<ul>
<li>航行速度北向分量<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>v</mi><mi>N</mi></msub></mrow><annotation encoding="application/x-tex">v_N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
</ul>
<p>引起地理坐标 系绕平行于地理东-西方向的地心轴相对地球坐标系转动，角速度为<img src="http://cos.pansis.site/202309142254186.png" alt="image-20230914225451146" style="zoom:33%;" /></p>
<img src="http://cos.pansis.site/202309142255525.png" alt="image-20230914225506495" style="zoom: 50%;" />
<ul>
<li>航行速度东向分量<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>v</mi><mi>E</mi></msub></mrow><annotation encoding="application/x-tex">v_E</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.32833099999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.05764em;">E</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
</ul>
<p>引起地理坐标系绕地球坐标系的极轴转动，其角速度</p>
<img src="http://cos.pansis.site/202309142323208.png" alt="image-20230914232330159" style="zoom:33%;" />
<p>投影到地理坐标系上</p>
<img src="http://cos.pansis.site/202309142315399.png" alt="image-20230914231520354" style="zoom: 50%;" />
<img src="http://cos.pansis.site/202309142324281.png" alt="image-20230914232450237" style="zoom:33%;" />
<h4 id="3-地球坐标系相对惯性坐标系的运动角速度">3、地球坐标系相对惯性坐标系的运动角速度</h4>
<p>地球坐标系相对惯性坐标系的转动 是由地球自转（角速度<span class="katex"><span class="katex-mathml"><math><semantics><mrow><msub><mi>w</mi><mrow><mi>i</mi><mi>e</mi></mrow></msub></mrow><annotation encoding="application/x-tex">w_{ie}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>）引起的</p>
<img src="http://cos.pansis.site/202309142307497.png" alt="image-20230914230737455" style="zoom:33%;" />
<h4 id="4-总角速度">4、总角速度</h4>
<img src="http://cos.pansis.site/202309142325110.png" alt="image-20230914232520050" style="zoom: 43%;" />
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